Religious leaders and faith-based organizations responded to Thursday's Supreme Court decision on health care, calling it alternately a "triumph of the common good" and "deeply wrong."

"This is an important victory for millions of uninsured people in our country and ultimately a triumph of the common good," Jim Wallis of the national interfaith social justice group Sojourners said on the group's website, though he cautioned that more work has yet to be done.

The U.S. Conference of Catholic Bishops used the decision to reiterate its objections to the law, namely government funding for abortions, the lack of a conscience exemption and the failure to provide equal coverage to immigrants.

"The decision of the Supreme Court neither diminishes the moral imperative to ensure decent health care for all, nor eliminates the need to correct the fundamental flaws (in the law)," the bishops said in a statement.

The bishops' conference has been arguing for months against what it sees as a growing encroachment by the government into the affairs of religious groups. It argues that requiring faith-based organizations other than houses of worship to offer no-cost contraceptives is a violation of religious liberty. It vowed Thursday to continue to push for changes in the law.

Thursday's decision upheld the key provisions of President Barack Obama's health care overhaul, most notably the requirement that people have health insurance after 2014. But the justices made it clear that they were not addressing the First Amendment issues making their way through the courts.

"A mandate to purchase a particular product would be unconstitutional if, for example, the edict impermissibly abridged the freedom of speech, interfered with the free exercise of religion, or infringed on a liberty interest protected by the due process clause," Justice Ruth Bader Ginsburg said in a separate opinion.

Public-interest law firms said Thursday they would continue those First Amendment challenges to key elements of the law.

"If the First Amendment means anything, it means you can't force monks and nuns to pay for somebody's contraception bill," said Emily Hardman of the Becket Fund for Religious Liberty, which represents religious organizations.

However, many religious organizations from across the faith spectrum hailed the decision as long overdue. They long have lobbied for reform, calling access to health care a basic human right.

In Milwaukee, where faith leaders and advocates have held prayer vigils and sent representatives to Washington to lobby for reform, the Rev. Dennis Jacobsen of Incarnation Lutheran Church called Thursday's decision a sacred moment that hit close to home.

A few years ago, Jacobsen said, just as the health care vigils were starting, a 30-year-old man in his congregation died because his cancer was diagnosed too late.

"I do have this sense that this was sort of a sacred moment in a secular chamber," Jacobsen, who heads the national clergy caucus for the advocacy group Gamaliel, said of the Supreme Court decision.